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Optimal Shape Design for Elliptic Systems

  • Olivier┬áPironneau

Part of the Springer Series in Computational Physics book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Olivier Pironneau
    Pages 1-15
  3. Olivier Pironneau
    Pages 16-29
  4. Olivier Pironneau
    Pages 30-44
  5. Olivier Pironneau
    Pages 45-67
  6. Olivier Pironneau
    Pages 81-98
  7. Olivier Pironneau
    Pages 99-120
  8. Olivier Pironneau
    Pages 121-142
  9. Olivier Pironneau
    Pages 143-162
  10. Back Matter
    Pages 163-168

About this book

Introduction

The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).

Keywords

Design Diskretisation Elliptische Differentialgleichung Konstruktion Optimale Regelung boundary element method calculus of variations differential equation fields finite element method numerical method partial differential equation simulation solution system

Authors and affiliations

  • Olivier┬áPironneau
    • 1
  1. 1.Centre Scientifique et Polytechnique, Departement de MathematiquesUniversite Paris-NordVilletaneuseFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87722-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-87724-7
  • Online ISBN 978-3-642-87722-3
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site